PHYSICAL REVIEW LETTERS 126, 091601 (2021)

Searching for Solar Using Data from the Sudbury Neutrino Observatory

Aagaman Bhusal ,1,2 Nick Houston ,3,* and Tianjun Li1,2 1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, China 3Institute of Theoretical Physics, Faculty of Science, Beijing University of Technology, Beijing 100124, China (Received 20 April 2020; accepted 1 February 2021; published 2 March 2021)

We explore a novel detection possibility for solar axions, which relies only on their couplings to nucleons, via the -induced dissociation of deuterons into their constituent neutrons and protons. An opportune target for this process is the now-concluded Sudbury Neutrino Observatory (SNO) experiment, which relied upon large quantities of heavy water to resolve the solar neutrino problem. From the full SNO 3 ≡ 1 − dataset we exclude in a model-independent fashion isovector axion-nucleon couplings jgaNj 2 jgan −5 −1 gapj > 2 × 10 GeV at 95% C.L. for sub-MeV axion masses, covering previously unexplored regions of the axion parameter space. In the absence of a precise cancellation between gan and gap this result also exceeds comparable constraints from other laboratory experiments, and excludes regions of the parameter space for which astrophysical constraints from SN1987A and neutron star cooling are inapplicable due to axion trapping.

DOI: 10.1103/PhysRevLett.126.091601

Introduction.—Arising straightforwardly as a minimal experimental convenience, most of the existing axion extension of the standard model, and in particular the literature rests similarly on axion-photon interactions. Peccei-Quinn solution of the strong CP problem [1–3], We will in the following instead turn attention to a less axions and axionlike particles (ALPs) occupy a rare focal well-explored corner of the parameter space, and, in point in theoretical physics, in that they are also simulta- particular, the axion-nucleon interactions neously a generic prediction of the exotic physics of string and M theory compactifications [4,5]. Despite the profound 1 μ 1 μ L ¼ g ð∂μaÞn¯γ γ5n þ g ð∂μaÞp¯ γ γ5p; ð1Þ differences between these contexts the resulting axion 2 an 2 ap properties are largely universal, creating an easily charac- terizable theoretical target. which can be reexpressed in terms of the neutron-proton As typically light, long-lived pseudoscalar particles they doublet N ¼ðn; pÞ as can also influence many aspects of cosmology and astro- 1 physics, leading to a wealth of observational signatures [6]. ¯ μ 1 3 L ¼ ð∂μaÞNγ γ5ðg I þ g τ3ÞN; ð2Þ In particular, they provide a natural candidate for the 2 aN aN mysterious comprising much of the mass of our visible universe [7,8], and as such are a focal point of where the isoscalar and isovector couplings are, respec- 1 2 3 − 2 intense ongoing investigation [9]. tively, gaN ¼ðgan þ gapÞ= , gAN ¼ðgan gapÞ= , and Fortuitously, our own Sun should provide an intense and τ3 ¼ diagð1; −1Þ. Although we will not make use of this readily available axion flux from which much of the here, if required integration by parts can be used to recast corresponding parameter space can be constrained. At this into present, the strongest resulting constraint is provided by L − ¯ γ 1 3 τ the CAST experiment [10], which relies upon the Primakoff ¼ iaN 5mNðgaNI þ gaN 3ÞN; ð3Þ conversion of axions into photons in a background mag- netic field. Presumably for reasons of observational and where mN ¼ diagðmn;mpÞ. We also emphasise here that although we consider axion-nucleon interactions, we are not assuming a QCD axion specifically. There are comparatively few constraints on axion- nucleon interactions, arising primarily from considerations Published by the American Physical Society under the terms of of SN1987A [11–14] and neutron star (NS) observations the Creative Commons Attribution 4.0 International license. – Further distribution of this work must maintain attribution to [15 18], experimental searches for new spin-dependent the author(s) and the published article’s title, journal citation, forces [19–25] and time dependent nuclear electric dipole and DOI. Funded by SCOAP3. moments [26]. It should, however, be noted that the overall

0031-9007=21=126(9)=091601(7) 091601-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 126, 091601 (2021) paradigm of axion constraints derived from SN1987A has The constant of proportionality is the probability for a been called into question [27,28]. given M1 nuclear transition to result in axion rather than The CASPER experimental program is also searching photon emission, for axion dark matter via nuclear interactions [29–31], and Γ 1 2 β 1 3 2 3 similar considerations have led recently to novel constraints a ≃ mn gaN þ gaN pa 2 ; ð6Þ from existing comagnetometer data [32]. Γγ 2πα1 þ δ ðμ0 − 0.5Þβ þ μ3 − η pγ Limits also exist from rare meson decays [33] and dedicated solar axion experiments which rely only where α is the fine structure constant, δ2 ¼ E=M is the upon nuclear couplings [34–39],however,astheseare relative probability for E and M transitions, we set model dependent we will not consider them going mn ¼ mp, and μ0 ¼ μp þ μn ≃ 0.88 and μ3 ¼ μp − μn ≃ forward. 4.71 are, respectively, the isoscalar and isovector nuclear As we will demonstrate, there is also an entirely novel magnetic moments, and pa=γ are the axion-photon and model-independent constraint arising from axions momenta [41]. Dependence on specific nuclear matrix emitted during nuclear transitions inside the Sun, which elements enters through β and η. can be detected on Earth through the M1 process In Eq. (5), the M1-type transitions associated with axion emission correspond to capture of protons with zero orbital a þ d → n þ p; ð4Þ momentum. The probability of this occurring at a proton energy of 1 keV has been measured and found to be 0.55 [42], implying δ2 0.82. Since capture from the S state where d is a deuteron. A particularly opportune target for ¼ corresponds to an isovector transition, we can assume the this mechanism is the now-concluded Sudbury Neutrino βg1 contribution to Eq. (6) is negligible and, to a good Observatory (SNO) experiment, which relied upon a large aN approximation, also ignore everything other than μ3 in the quantity of deuterium to resolve the solar neutrino problem denominator [43], leading to [40]. The possibility of using deuterium for axion detection was first noted by Weinberg in Ref. [2]. Γ 1 m2 g3 2 p 3 After detailing the corresponding axion flux and inter- a ≃ n aN a : Γ 2πα1 δ2 μ ð7Þ action cross section for Eq. (4) next, we then compute the γ þ 3 pγ resulting axion-induced event rate in SNO and derive constraints therefrom. Conclusions and discussion are Following Ref. [44] this provides the flux at Earth due to presented in closing. Eq. (5), Solar axion flux.—While axions can in general be ϕ ≃ 3 23 1010 2 3 2 3 −2 −1 produced within stars by a number of processes, such as a . × mnðgaNÞ ðpa=pγÞ cm s : ð8Þ Primakoff conversion, electron bremsstrahlung, and Compton scattering, we are primarily interested here in As this component of the solar axion flux has already their production via low-lying nuclear transitions. This is been well explored by the Borexino and CAST experiments primarily because the threshold for deuterium dissociation via a number of detection channels [44,45], we will in the via Eq. (4) is 2.2 MeV, and so only solar axions arising following focus only on the previously unexplored detec- from nuclear transitions will have sufficient energy. tion channel provided by deuterium (4). — However, there is also secondary benefit in so doing Axiodissociation cross section. We now construct the “ ” in that both emission and detection will rely only upon cross section for the axiodissociation process a single axion-nucleon coupling, allowing a model- → independent constraint of general applicability. a þ d n þ p; ð9Þ Of the nuclear transitions occurring inside the sun, the most intense axion flux is provided by with threshold energy 2.2 MeV. For reasons of clarity and brevity we give a relatively simple derivation of this quantity, postponing more thorough study to the future. → 3 γ 5 5 p þ d He þ ð . MeVÞ; ð5Þ Details of the corresponding nuclear physics are found in Refs. [46,47]. where an axion substitutes for the emitted . In Working in the rest frame of the initial state deuteron, the the standard solar model (SSM) this constitutes the second number of events we expect is stage of the pp solar fusion chain, with the first stage → þ ν provided by the two reactions p þ p d þ e þ e and Ne ¼ σϕNdT; ð10Þ − p þ p þ e → d þ νe. As the deuterons produced via this first stage capture protons within τ ≃ 6 s, the axion flux where ϕ is the incoming flux, Nd the number of targets and resulting from Eq. (5) can be expressed in terms of the T the time, we can rearrange for a single deuteron to give known pp neutrino flux. σ ¼ðV=viÞðNe=TÞ, where we have used the fact that for a

091601-2 PHYSICAL REVIEW LETTERS 126, 091601 (2021) single incoming axion ϕ ≡ nivi ¼ vi=V. No integration where m ≃ mn=2 is the reduced mass, r is the distance over energy is required since thermal broadening is between nucleons, ED ¼ 2.2 MeV the binding energy of negligible relative to the axion energy at hand. the deuteron, and ψ and V are functions of r only due to the Identifying Ne=T as the transition rate per unit time, we spherical symmetry of the presumed S-wave ground state. can make use of Fermi’s golden rule to write For the simplest possible approximation we can take V0 corresponding to a delta function potential at the origin, 2πV dn σ ¼ jhfjH jiij2ρðkÞ; ρðkÞ¼ ; ð11Þ which then yields v I dE i k 1 −αr ψ 3 ¼ pffiffiffiffiffiffiffiffiffiffi uðrÞχ3;uðrÞ¼Ne ; ð19Þ where the initial and final states are 4πr2 ffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi 3 ; 1 ;0 p p jii¼jS1 qi; jfi¼jS0 i; ð12Þ where N ¼ 2α and α ¼ mnERD, which satisfies the normalization condition hψjψi¼ ψ ψdV ¼ 1. The spin 3 a deuteron in the S1 ground state and an incoming axion, of the triplet is encoded in the eigenfunction 1 and the continuum S0 state, while Eq. (2) gives the 8 nonrelativistic interaction Hamiltonian > ↑ ↑ 1 <> jn p i Sz ¼þ 1 ↑ ↓ ↓ ↑ 1 χm pffiffi 0 ≃ 1 3 τ ∇⃗ σ⃗ 3 ¼ 2 ðjn p iþjn p iÞ Sz ¼ ; ð20Þ HI ðgaNI þ gaN 3Þ a · : ð13Þ > 2 :> ↓ ↓ jn p i Sz ¼ −1 We can expand in momentum modes via where S is the z component of the spin. 1 X 1 z aðxÞ¼pffiffiffiffi pffiffiffiffiffiffiffiffiffi ½aðq0Þeiq0·x þ a†ðq0Þe−iq0·x; ð14Þ The eigenfunction of the outgoing singlet is 2 0 V q0 Eq rffiffiffiffi 1 2 ψ 0 ¼ pffiffiffiffiffiffiffiffiffiffi jðrÞχ0;jðrÞ¼ sinðkr þ δ0Þ; ð21Þ so that due to the raising operation h0jaðq0Þ¼hq0j, 4πr2 L the axion part of the matrix element contains 0 δ h0jaðq Þjqi¼δqq0 , which removes the summation over where 0 is the s-wave phaseffiffiffi shift produced by the singlet p ↑ ↓ ↓ ↑ modes. Taking the derivative to get a factor of q⃗, we then potential and χ0 ¼ð1= 2Þðjn p i − jn p iÞ. With the have boundary conditionR kL þ δ0 ¼ nπ it is straightforward to 2 check that jψ 0j dV → 1 as L → ∞. We can then write i pffiffiffiffiffiffiffiffiffiffiffi 1 1 3 τ σ⃗ ⃗ iq·x 3 Z hfjHIjii¼ h S0jðgaNI þ gaN 3Þ · qe j S1i; 8EqV 1 3 h S0jqˆ ·ðσ⃗n −σ⃗pÞj S1i¼ jðrÞ uðrÞ½χ0;qˆ ·ðσ⃗n −σ⃗pÞχ3dr; ð15Þ ð22Þ where the exponential factor can be neglected as a long- wavelength approximation. To account for the isospin where ðψ; χÞ denotes the usual inner product for spinors. structure we can rewrite For the r-dependent piece we have Z rffiffiffiffi 1 3 1 3 ðg I þ g τ3Þσ⃗¼ g ðσ⃗ þ σ⃗Þþg ðσ⃗ − σ⃗Þ; ð16Þ 2 N½α sinðδ0Þþk cosðδ0Þ aN aN aN n p aN n p jðrÞuðrÞdr ¼ : ð23Þ L k2 þ α2 where the first term gives zero acting on the outgoing singlet state, since in that case the neutron and proton spins We can further introduce the singlet scattering length are antialigned, so that we then have as ¼ −1=k cotðδ0Þ¼−23.7 fm, to yield Z rffiffiffiffi ijq⃗jg3 2 1 − α pffiffiffiffiffiffiffiffiffiffiffiaN 1 ˆ σ⃗ − σ⃗ 3 Nkð asÞ hfjHIjii¼ h S0jq · ð n pÞj S1i: ð17Þ jðrÞ uðrÞdr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð24Þ 8E V 2 2 2 2 q L ðk þ α Þ 1 þ k as

2 To evaluate this expression fully, we need to solve the The spin-dependent factor in jhfjHIjiij , given that we Schrödinger equation for the deuteron wave function. mustP average over all the incoming deuteron polarizations, Although in principle a two-body problem, we can reduce 1 χ σ⃗ − σ⃗ χm 2 is 3 m jð 0;e· ð n pÞ 3 Þj , where we sum over all this to a one-body problem satisfying possible spin states of the triplet ground state. Considering σ⃗ 2 the z component of acting on the spin-dependent part of 1 1 ∂ σz ↑ ↑ σz ↓ − ↓ ½rψðrÞ þ ½E − VðrÞψðrÞ¼0; ð18Þ the wave function, j i¼j i and j i¼ j i so that 2m r ∂r2 D for the singlet state of the deuteron we have

091601-3 PHYSICAL REVIEW LETTERS 126, 091601 (2021)

1 2 of neutron thermalization, which negates sensitivity to the ðσ − σ Þz pffiffiffiðjn↑p↓i − jn↓p↑iÞ ¼ pffiffiffiðjn↑p↓iþjn↓p↑iÞ; n p 2 2 spectral character of the input flux. More specifically, detection of either of these pheno- ð25Þ mena rests upon the liberated neutron, once sufficiently thermalized, being recaptured. This can occur on a deu- which is twice the Sz ¼ 0 eigenfunction for the incoming 3 teron, resulting in the emission of a 6.25 MeV gamma ray, S1 state. As this implies ½χ0; ðσ⃗ − σ⃗ Þχ0¼0 we can 35 n p or alternatively in the phase II SNO dataset onto a Cl extend the sum to cover all possible states and then rewrite nucleus, resulting the emission of 8.6 MeV in gamma rays. the spin-dependent factor as 35 For the phase III dataset the Cl was removed and 1 X dedicated neutral current detectors (NCD) were introduced m m ½χ0; qˆ · ðσ⃗n − σ⃗pÞχ ½χ ; qˆ · ðσ⃗n − σ⃗pÞχ0: ð26Þ to enable non-Cherenkov detection of NC neutrons, via 3 3 m their capture onto He and the subsequent emission of a P proton-triton pair carrying 0.764 MeVof energy [48]. Since χm χm 1 Recognizing the insertion of m j ih j¼ , this is neutron capture cross sections are suppressed by their 1 4 velocity, these processes will in general only occur once 2 most of the initial kinetic energy has been lost, rendering fχ0; ½qˆ · ðσ⃗n − σ⃗pÞ χ0g¼ ; ð27Þ 3 3 SNO likely unable to distinguish between axion and ði jÞ ij neutrino-induced dissociated events. where we have used σ⃗χ0 ¼ −σ⃗ χ0 and σ σ ¼ δ . n p While this apparent loss of spectral information seems to From the boundary condition kL þ δ0 ¼ nπ we have a remove the possibility of leveraging the monoenergetic single state for each n, so that the number of outgoing states of the axion flux to gain greater sensitivity, it does between k and k þ dk is nonetheless simplify the required data analysis. Following the approach employed in Ref. [49], we can 1 dδ0 L write the total number of dissociation events seen by SNO dn ¼ π L þ dkjL→∞ ¼ π dk: ð28Þ dk as Z Given that dk=dEk ¼ 1=vf, from Eq. (11) we then have exp ϕ ξ σ N ¼ Na þ NdT SSM dEν ðEνÞ NC; ð32Þ 2VL σ ¼ jhfjH jiij2: ð29Þ v v I ϕ 5 60 0 66 106 −2 −1 i f where SSM ¼ð . . Þ × cm s is the pre- pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dicted value of the 8B solar neutrino flux in the B16-GS98 ⃗ γ 2 ⃗ − Using qc ¼ m0c vi ¼ Eavi and jkj¼ mnðEa EDÞ, standard solar model [50], with spectral shape parametrized qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi via 2 ⃗α 1 − α 2 σ 3 2 2 − 2 jkj ð asÞ ¼ ðgaNÞ mn Ea ma 2 2 2 2 2 : ð30Þ 2.75 2 3 ðk þ α Þ 1 þ k a −6 Eν Eν s ξðEνÞ¼8.52 × 10 15.1 − ; ð33Þ MeV MeV Data analysis.—Given the axion flux and cross section σ provided previously, we can then calculate the axion- and NC the neutral current neutrino-deuteron interaction induced event rate in the detector via Eq. (10).Itisof cross section [51]. As the resulting flux inferred by SNO course important to emphasize that the original purpose of assumes that these events arise only due to NC interactions, the deuterium in SNO was to observe the neutral current exp (NC) process ϕ ≡ R N SNO ξ σ ; ð34Þ NdT dEν ðEνÞ NC νx þ d → n þ p þ νx; ð31Þ and we can then write which could then, in concert with measurements of the ϕ σ electron neutrino flux, conclusively betray the presence of ϕ ϕ R a d SNO ¼ SSM þ ξ σ ; ð35Þ solar neutrino flavour oscillations. As the final state dEν ðEνÞ NC neutrino is invisible to the detector, the signature of this process is at first sight identical to that of Eq. (9). where no integration over energy is required since thermal Of course one key difference exists in that the 5.5 MeV broadening is negligible relative to the axion energy axions produced via Eq. (5) are monoenergetic, while the at hand. 8B neutrinos driving Eq. (31) have a continuous energy Since axion and neutrino-induced dissociations cannot spectrum with an endpoint near 15.8 MeV. However these be distinguished by SNO, the former can lead to an spectral differences are largely washed out by the process excess of events over the SSM expectation, and the

091601-4 PHYSICAL REVIEW LETTERS 126, 091601 (2021)

Variant QCD axion models may of course differ substan- tially from this benchmark [54]. Constraints on gan are also shown, if we assume no precise cancellation between gan and gap then any limit on 3 gaN is equivalent to a limit on both gan and gap. This assumption is not too restrictive; in the analysis of Ref. [55] this cancellation requirespffiffiffi a DFSZ-typepffiffiffi model with the specific tuning tan β ≃ 2 or 1= 2. This being the case our result can also exceed compa- rable constraints from other laboratory experiments, and exclude regions of the parameter space for which astro- physical constraints from SN1987A and NS cooling are inapplicable due to axion trapping, where axions cannot free stream and contribute to anomalous cooling as they do in other regions of the parameter space. The latter con- straints, which in any case share some degree of degeneracy with the SN1987A case, are not included in Fig. 1 due to model dependence and the unknown shape of the exclusion FIG. 1. 95% C.L. constraint on the isovector axion-nucleon region for non-negligible axion masses. 3 — coupling gaN arising from axion-induced dissociation of deu- Conclusions and discussion. The axion is a notably terium at SNO (blue). Following Refs. [44,52] we have imposed a well-motivated aspect of physics beyond the standard “ ” 3 ∼ 10−3 −1 solar trapping upper bound of jgaN j GeV , where model, and as such has been a topic of much investigation axions interact sufficiently strongly to be trapped within the 3 in recent years. Nonetheless, a large majority of these sun and hence escape detection. Also shown is the gaN -sensitive studies are based upon the interactions of axions with component of the SN1987A constraint from [11] (dark gray) electromagnetism, leaving their couplings to nucleons and arising from additional event counts at Kamiokande, even though this is not strictly comparable to our result due to dependence on other species comparatively less well explored. couplings other than g3 . In the absence of a precise cancellation In this Letter we have established a novel detection aN channel sensitive to precisely one of these couplings, our result also limits gan and gap individually, so constraints on the former are provided as a visual reference. These include relying upon the ability of suitably energetic axions to SN1987A cooling [14] (light green), SN1987A counts [11] (light dissociate deuterons into their constituent neutrons and gray), and the nonobservation of new forces [19,25] (dark green). protons. In concert with the 5.5 MeV solar axion flux Constraints which rely on the axion comprising all of the arising from the p þ d → 3He þ a process, one can then observed dark matter are also outlined (nuclear spin precession derive a model-independent constraint on the isovector in cold neutrons/Hg [26], CASPER [30], CASPER-ZULF [31] 3 3 axion-nucleon coupling gaN. A particularly opportune and old comagnetometer data [32]). The QCD axion band for gaN is given in yellow. target for this search strategy is the now-completed SNO experiment, which relied upon large quantities of deu- terium to resolve the solar neutrino problem. product ϕaσd is then constrained by the combined analysis Having derived the corresponding axiodissociation cross of all three phases of SNO data, which yields section, from the full SNO dataset we exclude regions ϕ 5 25 0 20 106 −2 −1 3 2 10−5 10−3 −1 SNO ¼ð . . Þ × cm s [48],wherewe where jgaNj is between × and GeV , for have added errors in quadrature. Requiring that the axion masses up to ∼5.5 MeV, covering previously ϕ − ϕ ð SNO SSMÞ confidence interval not exceed 95% C.L. unexplored regions of the axion parameter space. This limits then provides the exclusion presented in Fig. 1. comes with the added benefit that we do not require any 3 2 10−5 As can be seen, we exclude jgaNj between × and assumptions about the nature of dark matter, or the 10−3 GeV−1, for axion masses up to ∼5.5 MeV. For larger astrophysics of SN1987A. couplings this improves upon the g3 -sensitive component If furthermore we assume no precise cancellation between aN 3 of the SN1987A constraint in Ref. [11] arising from gap and gan then any limit on gaN is equivalent to a limit on additional particle-emission counts at Kamiokande, even both gan and gap. In that case our result can exceed though this is not strictly comparable as the SN1987A comparable constraints from other laboratory experiments, 3 axion flux is not solely dependent on gaN. and exclude regions of the parameter space for which The QCD axion band bounded by the KSVZ and DFSZ astrophysical constraints from SN1987A and NS cooling 2 models with cos β ¼ 1 is also shown; the latter case we are inapplicable due to axion trapping. Constraints on gan=gap exclude for axion masses between 0.3 and 13 keV, although from SN1987A event counts can probe equally large cou- this region is in any case ruled out by astrophysical plings, but at the cost of a variety of associated assumptions considerations and direct results from PandaX-II [53]. and uncertainties related to the modeling of SN1987A.

091601-5 PHYSICAL REVIEW LETTERS 126, 091601 (2021)

These findings could conceivably be improved in the [15] A. Sedrakian, Axion cooling of neutron stars, Phys. Rev. D future via a more sophisticated estimation of the axio- 93, 065044 (2016). dissociation cross section; we have neglected relativistic [16] A. Sedrakian, Axion cooling of neutron stars. II. Beyond and finite-size corrections, along with D-state effects in the hadronic axions, Phys. Rev. D 99, 043011 (2019). deuteron ground state. The existence of other axion search [17] M. V. Beznogov, E. Rrapaj, D. Page, and S. Reddy, Constraints on axion-like particles and nucleon pairing in strategies which rely only upon nuclear couplings is also a dense matter from the hot neutron star in HESS J1731-347, topic of ongoing investigation. Phys. Rev. C 98, 035802 (2018). This work is supported by the National Key Research [18] K. Hamaguchi, N. Nagata, K. Yanagi, and J. Zheng, Limit and Development Program of China Grant on the axion decay constant from the cooling neutron star in cassiopeia A, Phys. Rev. D 98, 103015 (2018). No. 2020YFC2201504, by the Projects No. 11875062 [19] G. Vasilakis, J. M. Brown, T. W. Kornack, and M. V. and No. 11947302 supported by the National Natural Romalis, Limits on New Long Range Nuclear Spin- Science Foundation of China, and by the Key Research Dependent Forces Set with a K—He-3 Co-Magnetometer, Program of Frontier Science, CAS. A. B. was supported by Phys. Rev. Lett. 103, 261801 (2009). a Chinese Government Scholarship, and N. H. also [20] V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko, acknowledges the hospitality of the Center for High and C. Romero, Constraining axion-nucleon coupling Energy Physics at , where much of this constants from measurements of effective Casimir pressure work was completed. by means of micromachined oscillator, Eur. Phys. J. C 74, 2859 (2014). [21] V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko, and C. Romero, Constraints on axion-nucleon coupling constants from measuring the Casimir force between cor- *Corresponding author. rugated surfaces, Phys. Rev. D 90, 055013 (2014). [email protected] [22] E. Fischbach and D. E. Krause, Constraints on Light [1] R. D. Peccei and H. R. Quinn, Constraints imposed by CP Pseudoscalars Implied by Tests of the Gravitational Inverse conservation in the presence of instantons, Phys. Rev. D 16, Square Law, Phys. Rev. Lett. 83, 3593 (1999). 1791 (1977). [23] E. Masso, Bounds on the coupling of light pseudoscalars to [2] S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40, 223 nucleons from optical laser experiments, Phys. Rev. D 61, (1978). [3] F. Wilczek, Problem of Strong P and T Invariance in the 011701(R) (1999). Presence of Instantons, Phys. Rev. Lett. 40, 279 (1978). [24] V. M. Mostepanenko, Progress in constraining axion and [4] P. Svrcek and E. Witten, Axions in string theory, J. High non-Newtonian gravity from the Casimir effect, Int. J. Mod. Energy Phys. 06 (2006) 051. Phys. A 31, 1641020 (2016). [5] A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, [25] E. G. Adelberger, B. R. Heckel, S. Hoedl, C. D. Hoyle, D. J. and J. March-Russell, String axiverse, Phys. Rev. D 81, Kapner, and A. Upadhye, Particle Physics Implications of a 123530 (2010). Recent Test of the Gravitational Inverse Sqaure Law, Phys. [6] D. J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016). Rev. Lett. 98, 131104 (2007). [7] M. Dine and W. Fischler, The not so harmless axion, Phys. [26] C. Abel, N. J. Ayres, G. Ban, G. Bison, K. Bodek, V. Bondar Lett. 120B, 137 (1983). et al., Search for Axionlike Dark Matter through Nuclear [8] J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the Spin Precession in Electric and Magnetic Fields, Phys. Rev. invisible Axion, Phys. Lett. 120B, 127 (1983). X 7, 041034 (2017). [9] I. G. Irastorza and J. Redondo, New experimental [27] K. Blum and D. Kushnir, Neutrino signal of collapse- approaches in the search for axion-like particles, Prog. Part. induced thermonuclear supernovae: The case for prompt Nucl. Phys. 102, 89 (2018). black hole formation in SN1987A, Astrophys. J. 828,31 [10] V. Anastassopoulos et al. (CAST Collaboration), New (2016). CAST limit on the axion-photon interaction, Nat. Phys. [28] N. Bar, K. Blum, and G. D’Amico, Is there a supernova 13, 584 (2017). bound on axions?, Phys. Rev. D 101, 123025 (2020). [11] J. Engel, D. Seckel, and A. C. Hayes, Emission and [29] D. Budker, P. W. Graham, M. Ledbetter, S. Rajendran, and Detectability of Hadronic Axions from SN1987A, Phys. A. O. Sushkov, Proposal for a Cosmic Axion Spin Pre- Rev. Lett. 65, 960 (1990). cession Experiment (CASPEr), Phys. Rev. X 4, 021030 [12] J. S. Lee, Revisiting Supernova 1987A limits on axion-like- (2014). particles, arXiv:1808.10136. [30] T. Wu et al., Search for Axionlike Dark Matter with a [13] J. H. Chang, R. Essig, and S. D. McDermott, Supernova Liquid-State Nuclear Spin Comagnetometer, Phys. Rev. 1987A constraints on Sub-GeV dark sectors, millicharged Lett. 122, 191302 (2019). particles, the QCD axion, and an axion-like particle, J. High [31] A. Garcon, J. W. Blanchard, G. P. Centers, N. L. Figueroa, Energy Phys. 09 (2018) 051. P. W. Graham, D. F. J. Kimball, S. Rajendran, A. O. [14] P. Carenza, T. Fischer, M. Giannotti, and A. Mirizzi, Sushkov, Y. V. Stadnik, A. Wickenbrock, T. Wu, and D. Improved axion emissivity from a supernova via nucleon- Budker, Constraints on bosonic dark matter from ultralow- nucleon bremsstrahlung, J. Cosmol. Astropart. Phys. 10 field nuclear magnetic resonance, Sci. Adv. 5, eaax4539 (2019) 016; 05 (2020) E01. (2019).

091601-6 PHYSICAL REVIEW LETTERS 126, 091601 (2021)

[32] I. M. Bloch, Y. Hochberg, E. Kuflik, and T. Volansky, [43] T. W. Donnelly, S. J. Freedman, R. S. Lytel, R. D. Peccei, Axion-like relics: New constraints from old comagneto- and M. Schwartz, Do axions exist?, Phys. Rev. D 18, 1607 meter data, J. High Energy Phys. 01 (2020) 167. (1978). [33] R. Essig, R. Harnik, J. Kaplan, and N. Toro, Discovering [44] G. Bellini et al. (Borexino Collaboration), Search for solar new light states at neutrino experiments, Phys. Rev. D 82, axions produced in pðd; 3HeÞA reaction with 113008 (2010). detector, Phys. Rev. D 85, 092003 (2012). [34] S. Moriyama, A Proposal to Search for a Monochromatic [45] S. Andriamonje et al. (CAST Collaboration), Search for Component of Solar Axions Using Fe-57, Phys. Rev. Lett. solar axion emission from 7Li and Dðp; γÞ3He nuclear 75, 3222 (1995). decays with the CAST γ-ray calorimeter, J. Cosmol. [35] M. Krcmar, Z. Krecak, M. Stipcevic, A. Ljubicic, and D. A. Astropart. Phys. 03 (2010) 032. Bradley, Search for invisible axions using Fe-57, Phys. Lett. [46] R. Sachs, Nuclear Theory (Addison Wesley, Cambridge, B 442, 38 (1998). MA, 1953). [36] M. Krcmar, Z. Krecak, A. Ljubicic, M. Stipcevic, and D. A. [47] E. Segre, Nuclei and Particles (W. A. Benjamin, Inc, Bradley, Search for solar axions using Li-7, Phys. Rev. D New York, 1965). 64, 115016 (2001). [48] B. Aharmim et al. (SNO Collaboration), Combined analysis [37] T. Namba, Results of a search for monochromatic solar of all three phases of solar neutrino data from the sudbury axions using Fe-57, Phys. Lett. B 645, 398 (2007). neutrino observatory, Phys. Rev. C 88, 025501 (2013). [38] A. V. Derbin, A. I. Egorov, I. A. Mitropol’sky, V. N. [49] J. A. Grifols, E. Masso, and S. Mohanty, Neutrino magnetic Muratova, D. A. Semenov, and E. V. Unzhakov, Search moments and photodisintegration of deuterium, Phys. Lett. for resonant absorption of solar axions emitted in B 587, 184 (2004). M1 transition in Fe-57 nuclei, Eur. Phys. J. C 62, 755 [50] N. Vinyoles, A. M. Serenelli, F. L. Villante, S. Basu, J. (2009). Bergström, M. C. Gonzalez-Garcia, M. Maltoni, C. Peña- [39] P. Belli et al., Search for Li-7 solar axions using resonant Garay, and N. Song, A new generation of standard solar absorption in LiF crystal: Final results, Phys. Lett. B 711,41 models, Astrophys. J. 835, 202 (2017). (2012). [51] S. Nakamura, T. Sato, V. P. Gudkov, and K. Kubodera, [40] J. Boger et al. (SNO Collaboration), The Sudbury neutrino Neutrino reactions on deuteron, Phys. Rev. C 63, 034617 observatory, Nucl. Instrum. Methods Phys. Res., Sect. A (2001). 449, 172 (2000). [52] G. Raffelt and L. Stodolsky, New particles from nuclear [41] F. T. Avignone, C. Baktash, W. C. Barker, F. P. Calaprice, reactions in the sun, Phys. Lett. 119B, 323 (1982). R. W. Dunford, W. C. Haxton, D. Kahana, R. T. Kouzes, [53] C. Fu, X. Zhou, X. Chen, Y. Chen, X. Cui, D. Fang et al., H. S. Miley, and D. M. Moltz, Search for axions from the Limits on Axion Couplings from the First 80 Days of Data 1115-kev transition of 65Cu, Phys. Rev. D 37, 618 (1988). of the PandaX-II Experiment, Phys. Rev. Lett. 119, 181806 [42] G. J. Schmid, B. J. Rice, R. M. Chasteler, M. A. Godwin, (2017). G. C. Kiang, L. L. Kiang, C. M. Laymon, R. M. Prior, D. R. [54] Y. Gao, T. Li, and Q. Yang, The minimal UV-induced Tilley, and H. R. Weller, The 2H(p→, gamma) 3He and 1H effective QCD axion theory, arXiv:1912.12963. (d →, gamma) 3He reactions below 80 keV, Phys. Rev. C 56, [55] L. Di Luzio, F. Mescia, E. Nardi, P. Panci, and R. Ziegler, 2565 (1997). Astrophobic Axions, Phys. Rev. Lett. 120, 261803 (2018).

091601-7